Whakaoti i te x^2-mx+21=0

$${ x }^{ 2 } -mx+21 = 0$$

Whakaoti mō m

$$m=x+\frac{21}{x}$$

$$x\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te x^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-mx+21=-x^{2}$$

Tangohia te 21 mai i ngā taha e rua.

$$-mx=-x^{2}-21$$

He hanga arowhānui tō te whārite.

$$\left(-x\right)m=-x^{2}-21$$

Whakawehea ngā taha e rua ki te -x.

$$\frac{\left(-x\right)m}{-x}=\frac{-x^{2}-21}{-x}$$

Mā te whakawehe ki te -x ka wetekia te whakareanga ki te -x.

$$m=\frac{-x^{2}-21}{-x}$$

Whakawehe -x^{2}-21 ki te -x.

$$m=x+\frac{21}{x}$$

Whakaoti mō x (complex solution)

$$x=\frac{\sqrt{m^{2}-84}+m}{2}$$

$$x=\frac{-\sqrt{m^{2}-84}+m}{2}$$

Whakaoti mō x

$$x=\frac{\sqrt{m^{2}-84}+m}{2}$$

$$x=\frac{-\sqrt{m^{2}-84}+m}{2}\text{, }|m|\geq 2\sqrt{21}$$